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You select a marble without looking and then put it back. If you do this 55 times, what is the best prediction possible for the number of times you will pick a purple marble?\newline\newline____\_\_\_\_ times

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Full solution

Q. You select a marble without looking and then put it back. If you do this 55 times, what is the best prediction possible for the number of times you will pick a purple marble?\newline\newline____\_\_\_\_ times
  1. Calculate Probability: First, we need to know the probability of picking a purple marble. Let's say there are 33 purple marbles out of 1010 total marbles.
  2. Calculate Expected Number: Calculate the probability of picking a purple marble: P(purple)=Number of purple marblesTotal number of marbles=310P(\text{purple}) = \frac{\text{Number of purple marbles}}{\text{Total number of marbles}} = \frac{3}{10}.
  3. Calculate Expected Number: Calculate the probability of picking a purple marble: P(purple)=Number of purple marblesTotal number of marbles=310P(\text{purple}) = \frac{\text{Number of purple marbles}}{\text{Total number of marbles}} = \frac{3}{10}. You repeat the action of picking a marble 55 times, each time replacing the marble. Calculate the expected number of times you pick a purple marble: Expected number = P(purple)×Number of trials=310×5=1.5P(\text{purple}) \times \text{Number of trials} = \frac{3}{10} \times 5 = 1.5.

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